Algebra Examples

$3 x + 4 y = - 12$ $y = - \frac{3}{2} x$

Step 1

Simplify $- \frac{3}{2} x$ .

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Step 1.1

Combine $x$ and $\frac{3}{2}$ .

$y = - \frac{x \cdot 3}{2}$

$3 x + 4 y = - 12$

Step 1.2

Move $3$ to the left of $x$ .

$y = - \frac{3 x}{2}$

$3 x + 4 y = - 12$

$y = - \frac{3 x}{2}$

$3 x + 4 y = - 12$

Step 2

Replace all occurrences of $y$ with $- \frac{3 x}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x + 4 y = - 12$ with $- \frac{3 x}{2}$ .

$3 x + 4 (- \frac{3 x}{2}) = - 12$

$y = - \frac{3 x}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 x + 4 (- \frac{3 x}{2})$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1.1

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

$3 x + 4 (\frac{- 3 x}{2}) = - 12$

$y = - \frac{3 x}{2}$

Step 2.2.1.1.1.2

Factor $2$ out of $4$ .

$3 x + 2 (2) (\frac{- 3 x}{2}) = - 12$

$y = - \frac{3 x}{2}$

Step 2.2.1.1.1.3

Cancel the common factor.

$3 x + 2 \cdot (2 (\frac{- 3 x}{2})) = - 12$

$y = - \frac{3 x}{2}$

Step 2.2.1.1.1.4

Rewrite the expression.

$3 x + 2 (- 3 x) = - 12$

$y = - \frac{3 x}{2}$

$3 x + 2 (- 3 x) = - 12$

$y = - \frac{3 x}{2}$

Step 2.2.1.1.2

Multiply $- 3$ by $2$ .

$3 x - 6 x = - 12$

$y = - \frac{3 x}{2}$

$3 x - 6 x = - 12$

$y = - \frac{3 x}{2}$

Step 2.2.1.2

Subtract $6 x$ from $3 x$ .

$- 3 x = - 12$

$y = - \frac{3 x}{2}$

$- 3 x = - 12$

$y = - \frac{3 x}{2}$

$- 3 x = - 12$

$y = - \frac{3 x}{2}$

$- 3 x = - 12$

$y = - \frac{3 x}{2}$

Step 3

Divide each term in $- 3 x = - 12$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 x = - 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

$y = - \frac{3 x}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

$y = - \frac{3 x}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{- 3}$

$y = - \frac{3 x}{2}$

$x = \frac{- 12}{- 3}$

$y = - \frac{3 x}{2}$

$x = \frac{- 12}{- 3}$

$y = - \frac{3 x}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 12$ by $- 3$ .

$x = 4$

$y = - \frac{3 x}{2}$

$x = 4$

$y = - \frac{3 x}{2}$

$x = 4$

$y = - \frac{3 x}{2}$

Step 4

Replace all occurrences of $x$ with $4$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - \frac{3 x}{2}$ with $4$ .

$y = - \frac{3 (4)}{2}$

$x = 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{3 (4)}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $4$ and $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $3 (4)$ .

$y = - \frac{2 (3 \cdot (2))}{2}$

$x = 4$

Step 4.2.1.1.2

Cancel the common factors.

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Step 4.2.1.1.2.1

Factor $2$ out of $2$ .

$y = - \frac{2 (3 \cdot (2))}{2 (1)}$

$x = 4$

Step 4.2.1.1.2.2

Cancel the common factor.

$y = - \frac{2 (3 \cdot (2))}{2 \cdot 1}$

$x = 4$

Step 4.2.1.1.2.3

Rewrite the expression.

$y = - \frac{3 \cdot (2)}{1}$

$x = 4$

Step 4.2.1.1.2.4

Divide $3 \cdot (2)$ by $1$ .

$y = - (3 \cdot (2))$

$x = 4$

$y = - (3 \cdot (2))$

$x = 4$

$y = - (3 \cdot (2))$

$x = 4$

Step 4.2.1.2

Multiply $- (3 \cdot (2))$ .

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Step 4.2.1.2.1

Multiply $3$ by $2$ .

$y = - 1 \cdot 6$

$x = 4$

Step 4.2.1.2.2

Multiply $- 1$ by $6$ .

$y = - 6$

$x = 4$

$y = - 6$

$x = 4$

$y = - 6$

$x = 4$

$y = - 6$

$x = 4$

$y = - 6$

$x = 4$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 6)$

Equation Form:

$x = 4, y = - 6$

Step 7